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DOI:
Journal of Software:2006.17(zk):38-45

均匀B样条基与DP-NTP基之间的转换与应用
成敏,王国瑾
(浙江大学 数学系,浙江 杭州 310027; 浙江工业大学 数学系,浙江 杭州 310032)
Conversion Between Uniform B-Spline Bases and DP-NTP Bases and Its Application
CHENG Min,WANG Guo-Jin
()
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Received:March 15, 2006    Revised:September 11, 2006
> 中文摘要: B样条基以其标准全正性和局部支柱性的长处,在曲线曲面构造中被广泛应用.而作为其特殊情况的均匀B样条,又因其操作简便等长处,对其的研究在工业造型设计方面也十分有意义.2003年,Delgado和Pe?a提出了另一类用标准全正基(DP-NTP基)构造的新曲线表示形式,这种曲线在求值运算中具有线性时间复杂度的明显优势,同时像B样条曲线那样具有模拟或保持控制多边形形状的保形性质,但没有形状局部可调性.为了使它们实现优势互补,并在不同的造型系统之间进行数据的交换和传递,给出了均匀B样条曲线与DP-NTP曲线的相互转换.实例表明,其结果可在CAD系统中,尤其在曲线曲面需要快速求值或形状局部可调的场合得到相当广泛的应用.
Abstract:B-spline basis is widely used in construction of curves and surfaces for its excellent property of being totally positive and locally adjustable. Uniform B-spline as a special case of B-spline is also worth researching for its convenience in operation in industry modeling. In 2003, Delgado and Pe?a had given another new form of curve, which is constructed by a new totally positive basis (DP-NTP basis). This kind of curve shows obvious advantage in computing, for the reason that it has linear complexity. Meanwhile, it has good shape preserving property. But regretfully it is not locally adjustable as how B-spline curves do. As to achieve the advantages of both, and as well make exchanging and transferring data possible between various systems, the conversion between uniform B-spline curves and DP-NTP curves is presented. Examples show that this result can be widely used in efficient evaluation of locally adjustable curves and surfaces.
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基金项目:Supported by the National Grand Fundamental Research 973 Program of China under Grant No.2004CB719400 (国家重点基础研究发展规划(973)); the National Natural Science Foundation of China under Grant No.60373033, 60333010 (国家自然科学基金) Supported by the National Grand Fundamental Research 973 Program of China under Grant No.2004CB719400 (国家重点基础研究发展规划(973)); the National Natural Science Foundation of China under Grant No.60373033, 60333010 (国家自然科学基金)
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成 敏,王国瑾.均匀B样条基与DP-NTP基之间的转换与应用.软件学报,2006,17(zk):38-45

CHENG Min,WANG Guo-Jin.Conversion Between Uniform B-Spline Bases and DP-NTP Bases and Its Application.Journal of Software,2006,17(zk):38-45